IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v20y2017i03ns0219024917500200.html
   My bibliography  Save this article

On The Calculation Of Risk Measures Using Least-Squares Monte Carlo

Author

Listed:
  • GIUSEPPE BENEDETTI

    (Fastval (FIS), 42 Rue Notre Dame des Victoires, 75002 Paris, France)

Abstract

The paper establishes a convergence result for the Least-Squares Monte Carlo method, applied to the estimation of risk measures (such as VaR) depending on the distribution of the future value of some derivative contract (or portfolio). We extend previous results in the literature by focusing on the specific case where the distribution of the underlying factors is known. In particular, we are able to remove the requirement of bounded conditional variance which is usually not satisfied by common financial models and payoffs at the cost of using a weaker notion of convergence. Our main result shows the convergence of the empirical distribution function when the number of simulations n and of basis variables m are jointly sent to infinity under certain conditions on the payoff and the basis. With a suitable choice of basis functions, we finally prove that convergence can be ensured when (m2ln m)/n → 0.

Suggested Citation

  • Giuseppe Benedetti, 2017. "On The Calculation Of Risk Measures Using Least-Squares Monte Carlo," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-14, May.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:03:n:s0219024917500200
    DOI: 10.1142/S0219024917500200
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024917500200
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024917500200?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Chen, Xiaohong & Christensen, Timothy M., 2015. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," Journal of Econometrics, Elsevier, vol. 188(2), pages 447-465.
    3. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    4. Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
    5. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    6. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Massimo Costabile & Fabio Viviano, 2020. "Testing the Least-Squares Monte Carlo Method for the Evaluation of Capital Requirements in Life Insurance," Risks, MDPI, vol. 8(2), pages 1-13, May.
    2. Weiß Christian & Nikolić Zoran, 2019. "An aspect of optimal regression design for LSMC," Monte Carlo Methods and Applications, De Gruyter, vol. 25(4), pages 283-290, December.
    3. Hongjun Ha & Daniel Bauer, 2022. "A least-squares Monte Carlo approach to the estimation of enterprise risk," Finance and Stochastics, Springer, vol. 26(3), pages 417-459, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hongjun Ha & Daniel Bauer, 2022. "A least-squares Monte Carlo approach to the estimation of enterprise risk," Finance and Stochastics, Springer, vol. 26(3), pages 417-459, July.
    2. Zhiyi Shen & Chengguo Weng, 2019. "A Backward Simulation Method for Stochastic Optimal Control Problems," Papers 1901.06715, arXiv.org.
    3. Marta Biancardi & Giovanni Villani, 2017. "Robust Monte Carlo Method for R&D Real Options Valuation," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 481-498, March.
    4. Hainaut, Donatien & Akbaraly, Adnane, 2023. "Risk management with Local Least Squares Monte-Carlo," LIDAM Discussion Papers ISBA 2023003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Zineb El Filali Ech-Chafiq & Pierre Henry-Labordere & Jérôme Lelong, 2021. "Pricing Bermudan options using regression trees/random forests," Working Papers hal-03436046, HAL.
    6. Denis Belomestny & Grigori Milstein & Vladimir Spokoiny, 2009. "Regression methods in pricing American and Bermudan options using consumption processes," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 315-327.
    7. Alessandro Gnoatto & Athena Picarelli & Christoph Reisinger, 2020. "Deep xVA solver -- A neural network based counterparty credit risk management framework," Papers 2005.02633, arXiv.org, revised Dec 2022.
    8. Belomestny, Denis & Milstein, Grigori N. & Spokoiny, Vladimir, 2006. "Regression methods in pricing American and Bermudan options using consumption processes," SFB 649 Discussion Papers 2006-051, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. Mingbin Ben Feng & Eunhye Song, 2020. "Efficient Nested Simulation Experiment Design via the Likelihood Ratio Method," Papers 2008.13087, arXiv.org, revised May 2024.
    10. Shuai Gao & Jun Zhao, 2016. "Pricing 50ETF in the Way of American Options Based on Least Squares Monte Carlo Simulation," Applied Finance and Accounting, Redfame publishing, vol. 2(2), pages 71-76, August.
    11. Lokman A. Abbas-Turki & Stéphane Crépey & Babacar Diallo, 2018. "Xva Principles, Nested Monte Carlo Strategies, And Gpu Optimizations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-40, September.
    12. Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, vol. 50(9), pages 1193-1203, September.
    13. Ikefuji, Masako & Laeven, Roger J.A. & Magnus, Jan R. & Muris, Chris, 2020. "Expected utility and catastrophic risk in a stochastic economy–climate model," Journal of Econometrics, Elsevier, vol. 214(1), pages 110-129.
    14. Lotfi Boudabsa & Damir Filipovi'c, 2022. "Ensemble learning for portfolio valuation and risk management," Papers 2204.05926, arXiv.org.
    15. Garcia, Diego, 2003. "Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1855-1879, August.
    16. Ma, Jin & Zhang, Jianfeng, 2005. "Representations and regularities for solutions to BSDEs with reflections," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 539-569, April.
    17. Mark Broadie & Weiwei Shen, 2016. "High-Dimensional Portfolio Optimization With Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-49, June.
    18. Farid AitSahlia & Manisha Goswami & Suchandan Guha, 2010. "American option pricing under stochastic volatility: an efficient numerical approach," Computational Management Science, Springer, vol. 7(2), pages 171-187, April.
    19. Vijay V. Desai & Vivek F. Farias & Ciamac C. Moallemi, 2012. "Pathwise Optimization for Optimal Stopping Problems," Management Science, INFORMS, vol. 58(12), pages 2292-2308, December.
    20. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2008. "Simulation-based pricing of convertible bonds," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 310-331, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijtafx:v:20:y:2017:i:03:n:s0219024917500200. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.